1935
Macromolecules 1992,25, 1935-1940
Optical Characterization of Ordering and Disordering of Block Copolymer Microstructure Karl Amundson,*Eugene Helfand, Sanjay S. Patel, and Xina Quan AT&T Bell Laboratories, Murray Hill, New Jersey 07974
Steven D. Smith The Procter and Gamble Company, Cincinnati, Ohio 45239 Received November 11, 1991; Revised Manuscript Received December 13, 1991
ABSTRACT: Phenomena associated with the order-disorder transition (ODT) of block copolymers have been studied optically. Observations have been made on symmetric polystyrene-b-poly(methy1methacrylate) diblock samples of two molecular weights. Ordering and disordering are clearly indicated by birefringence and a light intensity measurement sensitive to inhomogeneities in microscopic birefringence. The transition temperatures were compared to rheologically-determined ODT temperatures. The optical measurements point to complex behavior near the ODT, including an apparent -3 "C increase in the disorder temperature upon annealing as well as apparent gradual disorderingover a 5-7 "C temperature range. Optical measurements of this type would appear to be a valuable tool for noninvasive study of block copolymers.
Introduction The order-disorder transition (ODT) of block copolymers, as well as behavior around this transition, has been the focus of much theory and experiment.l-l0 It is of considerableinterest because of its relevanceto processing, and it is a model for the study of an unusual class of phase transitions.2-4 The primary means by which transitional behavior has been studied is by rheology4-8 and scattering?Joboth of which reflect the transition from an ordered to a disordered state. In this paper, we report optical measurements on symmetric polystyrene/poly(methyl methacrylate)diblock copolymer samplesnear the ODT. We have observed that a birefringence measurement and a light intensity measurement are sensitive indicators of ordering and disordering in these copolymers. In broad terms, the birefringence disappears when the material disorders and reappearswhen the material orders. The detailed behavior near the ODT is complex, however, and will be the focus of this paper. These optical measurements are sensitive to ordering,disordering,alignment of microstructure, and defect density and should provide information complementary to rheology and scattering on a wide variety of block copolymer systems. Birefringence and Block Copolymer Microstructure. Form birefringence, the birefringence due to an anisotropic composition pattern, has been observed in aligned, strongly phase-segregated styrene-isoprene block copolymer^^^-^^ and in polystyrene/poly(methyl methacrylate) block cop01ymers.l~ In this section, we develop a general expression for the form birefringence which is applicable to block copolymers near the ODT. In a block copolymer sample,the displacement field, D, is related to the electric field, E, through the relation D(r) = t(r) E(r) (1) where e(r) is the local dielectric constant, which is a function of the composition at position r and is evaluated by coarse-graining over a volume containing many monomers but over a length scale much smaller than molecular dimensions. Since ultimately the electric field we are considering is that of light, the dielectric constant and all subsequent ones defined must be the appropriate values for the frequence of light used. 0024-929719212225-1935$03.00/0
By averaging eq 1 over a scale larger than molecular dimensions but smaller than the length scale over which the ordered-phase microdomain pattern loses coherence, we can define an effective dielectric constant, t, associated with a region of coherence in the ordered phase:
-
-
D(r) = e(r)E(r) = =c.E(r)
(2)
where the bar denotes the spatial average. Because of a lack of rotational symmetry of the ordered-phase microdomain pattern, the effective dielectric constant must be expressed as a second-rank tensor. The effective dielectric constant can be determined by solvingthe Maxwell equation for the case where there are no free charges:
V-D = V.[c(r) E(r)l = 0 (3) Assume the local dielectric constant varies linearly with local composition,as expressed by the variable $(r),which is the deviation of the volume fraction of one component from its mean value. Below the transition, one expects a periodic lamellar pattern, ($), to emerge.'s2 (The angular bracketa indicate a time average over a time much larger than the lifetime of composition fluctuations but much smaller than the time over which the ordered-phase microdomain pattern changes.) Equations 2 and 3 can be solved to second order in (#) to yield (4)
where €1 and €2 are the dielectric constants of the two pure components (again evaluated at the frequency of light). is the dielectric constant in the limit of vanishing microdomain pattern and contains a contribution from the dynamic composition fluctuationswhose correlation length is much smaller than the wavelength of light. I is the identity matrix, and dk the unit wave vector of thz lamellar pattern. Using the relation n2 = c (in Gaussian units), n, 5 sezond order in ($), is the refractive index tensor, -
nl and n2 are the refractive indices of the pure components, 0 1992 American Chemical Society
Macromolecules, Vol. 25, No. 7, 1992
1936 Amundson et al. compensator
1laser light out
iris
insulation
Figure 1. Apparatus for optical measurements, The laser beam passed through a chopper and then through a polarizer (P)and a quarter-wave plate (X/4) to produce right-circular polarization. After the beam passed through the sample cell and compensator, a quarter-wave plate and polarizer filtered out right-circular polarization. The left-circularly-polarized portion of the beam was measured with a photodetector and a lock-in amplifier.
quartz windows
no the refractive index in the limit of vanishing microdomain pattern, and Ano the maximum form birefringence strength for complete microphase segregation (defined in the above expression). From refractive index data for polystyrene and poly(methy1 methacrylate) reported by Michel et al.,15Anofor a symmetricpolystyrene-b-poly(methyl methacrylate) copolymer is computed t o be -4.0 X at 160 "C and is expected to drop only slightly (-6%) upon heating to 260 "C. For light propagation at an angle 6 to Qk, eq 5 yields a form birefringence of
-
1laser light in
rJ+---l 0
' ''
RTD
N2 exhaust
skinless steel plate
Figure 2. Top and side cross-sectionalviews of the sample cell.
Anfom= 4Ar~'(3/)~sin2 0 (6) with a "fast" axis along the projection of hk in the plane -trajectory. In the limit of perpendicular to the optical strong phase segregation, ( $ ) 2 = l/.+,and eq 6 reduces to the familiar form birefringence of the symmetric "stackedplate" morphology.12J6 Light polarized along the "slow" axis will experience a phase retardation of magnitude
6 = 2 ~1A n- ' ( $ )sin2 ~ 6
sample
(7)
with respect to light polarized along the "fast" axis, where 1 is the optical path length and X is the wavelength of light in the medium (420 nm for 633-nm He-Ne laser light). If chain extension due to microphase separation is significant, molecular birefringence will also be present. This contribution can be very significant for stronglysegregated block copolymer lamellar systems12J4 but should be small near the ODT. If it is present, it will add an additional negative quantity to the already-negative form birefringen~e.'~J'-~~
Experimental Section Materials. Polystyrene/poly(methylmethacrylate) diblock copolymer samples were synthesized anionically. Their molecular weight averages were 37 OOO and 31 OOO (polydispersity indices 1.08 and 1.07, respectively), as determined by size exclusion chromatography using polystyrene standards. These are referred to as SM-37 and SM-31, respectively. Both copolymersare 53 vol % polystyrene as determined by lH NMR. Rheologicalmeasurement@ were made using a Rheometrics7700 dynamic mechanical spectrometer with a parallel-plate fixture. Electron micrographs reveal that these materials have a lamellar microstructure at low temperature. Optical Analysis. The optical apparatus is shown in Figure 1. The 632.8-nm He-Ne laser light was made right-circularly polarized by passage through a polarizer and quarter-waveplate. It then passed through the sample cell and a Babinet-Solei1 compensator. A quarter-wave plate and polarizer before the detector filtered out right-circularpolarization, and so the detector measured only left-circular polarization intensity. The phase retardation and orientation of the compensator were adjusted to minimize light intensity at the detector;the compensator readings then indicated the sample birefringence strength and principal axes. The minimized light intensity was also recorded. Imperfections in optical components introduced systematic errors in the birefringence strength measurements on the order of 30 mrad.
The sample cell is shown in Figure 2. The laser light passed through quartz windows and a rectangular channel in the center platform of the cell. Two rectangular windows contained the polymer samplewithin a 2-mm section of the channel. A stainless steel plate pressed tightly against the center platform made up the floor of the sample region. The temperature was controlled (*0.2 OC) with a thermally regulated nitrogen gas purge. A platinum resistance temperature detector bolted to the stainless steel plate from below was used to measure temperature and was calibrated with a thermocouple embedded in a polymer sample. The temperature of the sample cell was also calibrated against the Rheometrics dynamic mechanical spectrometer used in the rheological measurements. The time lag between temperature changes of the sample and the temperaturedetector reading was 20-25 a.
Results Figure 3 shows the low-frequency elastic moduli of both copolymers in oscillatory shear. (A full description of the rheology is presented in ref 20.) The ODT, signaled by a drop in the elastic modulus, is at 251 f 1 and 182 f 2 "C for SM-37and SM-31,respectively. Data were collected in the order of increasing temperature. Figures 4 and 5 show the birefringent phase retardation and minimized light intensity for SM-37 and SM-31 during slow cooling and subsequent slow heating. The cooling and heating rates were 0.2 OC/min near the transition region and somewhat faster far away from the transition region. At high temperature, the birefringence strength was a constant small value, and at low temperature it was nonzero and decreasing with increasing temperature. After the first thermal cycle, the SM-31 sample was heated a second time t o 180 "C, annealed for 5 h, and then very slowly heated (
